Some write as if this were true. The story is that after the New Classical counter revolution, Keynesian ideas could only be reintroduced into the academic mainstream by accepting a whole load of New Classical macro within DSGE models. This has turned out to be a Faustian bargain, because it has crippled the ability of New Keynesians to understand subsequent real world events.
Is this how it happened? It is true that New Keynesian models are essentially RBC models plus sticky prices. But is this because New Keynesian economists were forced to accept the RBC structure, or did they voluntarily do so because they thought it was a good foundation on which to build?
One way of looking at this (and I’ll argue at the end that it misses a key element) is to think about the individual components of models. If you do this, the Faustian bargain story looks implausible. Let’s start with the mainstream before the New Classical revolution. This was the famous post-war neoclassical synthesis popularised by Paul Samuelson, which integrated traditional Keynesian and Classical models in a common overall framework. While prices were sticky we were in a Keynesian world, but once prices had adjusted the world was Classical.
In terms of components, the RBC model is just the classical macromodel with two key additions. The first is rational expectations. The second is intertemporal optimisation by agents. (In non-jargon, it takes seriously the ability of agents to choose when they consume by saving or borrowing, rather than simply assuming they just consume a fixed proportion of their current income. This is often called the consumption smoothing model, because typically consumers smooth consumption relative to income e.g. by saving for retirement.) In both cases I do not think Keynesian economists were forced to adopt these ideas against their better judgement. Instead I think quite the opposite is true: both ideas were readily adopted because they appeared to be a distinct improvement on previous methods.
The key point here is that they were an improvement on previous practice. It does not mean that economists thought they were the final answer, or indeed that they were half adequate answers. Instead they were a better foundation to build on compared to what had gone before. I’ve argued this for rational expectations before, but I also think it is true for intertemporal consumption. I find it very difficult to think about more complex ideas, like liquidity constraints or precautionary saving, without starting with consumption smoothing.
I have talked about the real world events that convinced me of this, but here let me make the same point in a more informal way. When teaching on the Oxford masters programme, I give students a question. If they won a large sum, would they spend it over the next year, over the next few years, spend a significant proportion now but save the rest, or save nearly all. The last response is the answer given by the simple intertemporal model, but I argue that the first two responses make perfect sense if you are a credit constrained student. However I tell my audience that those who gave the first answer are not intending to do a PhD after finishing the masters, while those who gave the second are, because they are expecting the credit constraint to last longer. The serious point is that credit constrained consumers do not automatically consume all of a temporary increase in income. If the period over which income is higher is less than the period over which they expect to be constrained, they will smooth their additional consumption.
So, in terms of the components of New Keynesian models, I can see little that most modellers would love to junk if it wasn’t for those nasty New Classicals.  But what this ignores is methodology, and the fact that the RBC model is a microfounded Classical model. (By microfounded, I mean that every macroeconomic relationship has to be formally derived from optimisation by individual agents.) Yet here again, I doubt that most New Keynesian modellers adopted the microfoundations perspective against their better judgement. Instead I suspect most saw the power of the microfoundations approach (in analysing consumption, in particular), recognised the dangers in ad hoc theorising about dynamics (as in the traditional Phillips curve), and thought there was no contest.
The more interesting question is whether this has turned out to be a Faustian pact between macroeconomics and microfoundations ex post. To be more precise, by putting all our macroeconomic model building eggs in one microfounded basket, have we significantly slowed down the pace at which macroeconomists can say something helpful about the rapidly changing real world? That is a question I have written a lot about (e.g. here, and here) and no doubt will write more, but the key point I want to make now is this. If there was a Faustian bargain, I think we should acknowledge that most Keynesian economists agreed to it for good reasons, and that they were not forced into it by others.
 I must add a caveat here, although it is rather controversial. I think one sense in which RBC models have cast an annoying shadow is the idea that we must have models in which labour supply is endogenous. Often it would make things simpler if we could assume a fixed labour supply, and my own view is that for many issues we would lose little empirical relevance if we did so. Here I do think New Keynesians are too deferential to the always silly idea of trying to explain movements in unemployment as simply a labour supply choice.